I consider trisets one set, but I never triset exercises for the same muscle group. For instance, a common triset for me is incline DB press, pulldowns, pullovers. This hits three different muscles in one triset. I consider that one set and I do four of them.

I would be afraid that your method did not allow for adequate rest between sets.

I learned about supersets and trisets from reading Dave Draper, but I could definitely be wrong.

I would agree that I did not get adequate rest between sets, as my log shows how much less I lifted in the exercises compared with how much I usually lift. However, the pumped feeling is unmatched. Also, I hadn't experienced that much soreness in a long time, and that's something for me because I constantly add weight weekly. It felt like a hardcore workout indeed.